Stator/magnet swept area

Electric Motors and Controllers
fourbanger   100 W

Posts: 214
Joined: Jul 17 2014 10:09pm

Stator/magnet swept area

Trying to figure out the relation between the amount of surface area passing a magnet and the amount of power a motor can reasonably be expected to produce.

These figures are derived by calculating the stator diameter * 3.14 * stator width.

Here are some examples [numbers are in centimetres squared]:

225.29 1500W Leaf Hub Motor [20.5cm(dia.) * 3.14 * 3.5cm(width)]
131.88 40H Scooter Hub Motor [10.5 * 3.14 * 4.0]
62.01 450W GNG Mid Drive [7.9 * 3.14 * 2.5]
179.35 Mini Conhis Hub Motor [13.5 * 3.14 * 4.2]
98.91 8.5" Scooter Hub Motor [10.5 * 3.14 * 3.0
76.87 eZee Geared Hub Motor [13.6 * 3.14 * 1.8]

OK. Easy peasy, but all this tells me is how much stator surface area is passed by a given magnet for 1 rpm. So I need to factor in a rotational speed to get some idea of power produced, right?

Using the same examples:

225.29 1500W Leaf Hub Motor [20.5cm * 3.14 * 3.5cm] x 652rpm = 146892 [cm.sq. per minute]
131.88 40H Scooter Hub Motor [10.5 * 3.14 * 4.0] x 1000rpm = 131880
62.01 450W GNG Mid Drive [7.9 * 3.14 * 2.5] x 3000rpm = 186030
179.35 Mini Conhis Hub Motor [13.5 * 3.14 * 4.2] x 600rpm = 107610
98.91 8.5" Scooter Hub Motor [10.5 * 3.14 * 3.0 x 1000rpm = 98910
76.87 eZee Geared Hub Motor [13.6 * 3.14 * 1.8] x 937.5 = 72065.625

EDIT: Pretty sure the 1500W Leaf has .35mm lams but we're just going to pretend that it doesn't here...
: )

[RPM is derived from dividing 250hz (the frequency at which a motor with 0.5mm laminations begins to lose efficiency, apparently) by number of pole pairs multiplied by 60 (number of seconds in a minute)]

Ok, so, my question is: Is this an OK way to APPROXIMATE the amount of power produced by a given motor and, if not, why not? I know I'm omitting a bunch of things like magnet thickness, airgap, heat shedding and a whole whack of other details I don't even know about. But it would be neat if I could use numbers like these as a quick benchmark for performance.

What do you guys think?

Kind regards as always.
Last edited by fourbanger on Apr 09 2021 10:39am, edited 1 time in total.

mxlemming   100 W

Posts: 203
Joined: Jul 17 2020 7:56am

Re: Stator/magnet swept area

This sounds reasonable to me, bearing in mind all the extra factors you mentioned. I think it's fair to say that this produces an upper bound estimate of the possible power, poor copper fill, thick laminations, poor magnets etc... Will reduce this upper bound.

The goal of motor design should be to produce a geometry that maximizes the flux gap area and field strength as strong as possible in the gap while keeping the iron mass as low as possible and avoiding flux hot spots that prematurely saturate.
The Earth is flat. Flat flat flat. How would transistors work otherwise?

fourbanger   100 W

Posts: 214
Joined: Jul 17 2014 10:09pm

Re: Stator/magnet swept area

Oh yea! I definitely almost understood half of that last paragraph. I still have a LOT of reading to do concerning magnetic fields and lines of flux and, well, everything really. Would it be too presumptuous of me to speculate that it is all of those last issues mentioned that leads people towards axial flux motors?

mxlemming   100 W

Posts: 203
Joined: Jul 17 2020 7:56am

Re: Stator/magnet swept area

I'm not going to express too much certainty on this one, happy to stand corrected, but it doesn't seem to me that axial flux motors are fundamentally better at optimising that goal, and they present manufacturing challenges easily avoided by radial flux.

Imagine your flux gap is grid paper. Now imagine you have to connect all the squares of the grid together with squares a few cm away using string (to represent flux). Whether the paper is flat or rolled into a tube, there's no vast difference in the amount of string you need to make the connections. There might be small advantages but they'll be in the single digit% not 50% better/worse region.
The Earth is flat. Flat flat flat. How would transistors work otherwise?

everythingisawave   100 mW

Posts: 42
Joined: Sep 13 2016 8:01pm

Re: Stator/magnet swept area

I can't remember the exact equations, but I recall that rough estimations for comparison of machines can be done by making some starting assumptions about maximum current density and airgap flux density assuming that things have been optimized to make best use of the material, then from there it is possible to estimate torque for a given configuration. I got curious and went back to the seminal paper, as usual the earlier literature is the most readable:

Slemon, G. R. (1994). On the design of high-performance surface-mounted PM motors. IEEE Transactions on Industry Applications, 30(1), 134–140. doi:10.1109/28.273631

If you can't get acccess, this paper here explains the approach used briefly, and is freely downloadable:
https://ietresearch.onlinelibrary.wiley ... .2016.0179
Capture.PNG (81.78 KiB) Viewed 89 times
The values for airgap flux and linear current density are tricky to understand, but at least the general relationship is there, so you can figure out the overall trend.

spinningmagnets   100 GW

Posts: 11983
Joined: Dec 21 2007 10:27pm
Location: Ft Riley, NE Kansas

Re: Stator/magnet swept area

The entire swept face of the rotor and stator of an axial-flux can be working magnets plus electro-magnet material, but the motor mass near the center has trouble shedding heat. If width isn't a problem, you can stack more stators and rotors on the same shaft.

Zero motorcycles started out with Motenergy axial-flux motors, one rotor and two stators. Liquid cooling could not meet ther cost and reliability goals, so motor was to be air-cooled.

In the amount of space allotted for motor volume, they ended up with an inrunner radial flux, because it passively shed heat well. The highest possible temporary peak power was adequate on a light motorcycle, and continuous power at heat-shedding stasis was acceptable.

That being said, the radial-flux has a lot of unused air-space at its center.

spinningmagnets   100 GW

Posts: 11983
Joined: Dec 21 2007 10:27pm
Location: Ft Riley, NE Kansas

Re: Stator/magnet swept area

If you confine yourself to radial-flux in-runners, like the popular Leaf 35mm, MXUS 45mm, and QS 50mm wide stator examples, I agree that swept face area is a good indicator of power potential, if all other factors are the same. (These three examples use the same 205mm diameter lamination stacks)

The copper mass of the motor has an effect, but that is usually scaled in ratio with the swept face area.

Direct drive motors like this can take a LOT of peak amps for a short while, and any improvements you make that help heat-shedding will lengthen the amount of time you can use max amps. Ferro-fluid is cheap and it is a huge benefit to heat-shedding.

thepronghorn   1 kW

Posts: 315
Joined: Mar 27 2011 8:07pm
Location: Bay Area, California

Re: Stator/magnet swept area

Power is torque*rpm.

For torque, you're missing that the airgap area is only proportional to force. This force has to be multiplied by airgap radius to get torque.

Another quick benchmark you can use for torque performance is the "motor constant" (Km) which is Kt/sqrt(phase resistance). It is proportional to "torque per watt of copper loss". So a motor with twice the Km will make twice the torque for the same copper loss.

larsb   10 MW

Posts: 2025
Joined: Dec 10 2014 5:12am
Location: Gothenburg, Sweden

Re: Stator/magnet swept area

The values for airgap flux and linear current density are tricky to understand, but at least the general relationship is there, so you can figure out the overall trend.
Units need to be looked at so that they all go together but this is what i would do to estimate a motor from scratch from the equation:

Torque is force x lever
Torque lever r

Force is area x force per area
Airgap area 2*pi*r*l

Flux and resulting force per area are the difficult ones but could be estimated:
Airgap flux b can be calculated in a free program like FEMM or even estimated with one of the online magnet calculators like the one on k&j magnetics site

Linear current density represents the coil field, a simple estimation can be done from the saturation point of the lamination steel multiplied with the tooth neck area.

With some unit checks and possibly conversions you have the max torque but only for one position where angle between fields is 90 degrees (sin90=1 for max). Estimate that torque ripple lowers average max torque by 10% then the sin factor can be replaced with 0.9

Done

Note that this gives an estimation of max torque at start of steel saturation. Motors are driven above this point by the hotrodders and it’s not the absolute max torque. Also note that motor will not be able to output this torque for longer term. How long depends on cooling, thermal weight and efficiency and they are a bit harder to estimate.